Before the collision, the blue billiard ball (0.15 kg) is moving at a speed of 3 m/s to the right, while the green billiard ball (0.15 kg) is moving at a speed of 2 m/s to the left (in the opposite direction). After the collision, the blue ball comes to a complete stop, remaining in place, and the green ball continues to move to the left.
To find the speed of the green ball after the collision, we can use the principle of conservation of momentum. The total momentum before the collision is given by:
\[ \text{Momentum}{initial} = m{blue} \cdot v_{blue} + m_{green} \cdot v_{green} = (0.15 , \text{kg} \cdot 3 , \text{m/s}) + (0.15 , \text{kg} \cdot (-2 , \text{m/s})) = 0.45 , \text{kg m/s} - 0.30 , \text{kg m/s} = 0.15 , \text{kg m/s}. \]
After the collision, the blue ball is stationary, so its momentum contribution is 0. Therefore, the momentum of the green ball must equal the initial total momentum:
\[ 0.15 , \text{kg m/s} = 0.15 , \text{kg} \cdot v_{green, final}. \]
Solving for \( v_{green, final} \):
\[ v_{green, final} = \frac{0.15 , \text{kg m/s}}{0.15 , \text{kg}} = 1 , \text{m/s}. \]
This means the green ball moves to the left with a speed of 1 m/s after the collision.
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